A134889 a(n)=the largest sum of two nontrivial divisors of n, if any, whose product equals n; otherwise, a(n)=n.

1, 2, 3, 4, 5, 5, 7, 6, 6, 7, 11, 8, 13, 9, 8, 10, 17, 11, 19, 12, 10, 13, 23, 14, 10, 15, 12, 16, 29, 17, 31, 18, 14, 19, 12, 20, 37, 21, 16, 22, 41, 23, 43, 24, 18, 25, 47, 26, 14, 27, 20, 28, 53, 29, 16, 30, 22, 31, 59, 32, 61, 33, 24, 34, 18, 35, 67, 36, 26, 37, 71, 38, 73, 39

Offset

1,2

Comments

A divisor of n other than 1 or n is called nontrivial.

Links

Table of n, a(n) for n=1..74.

Example

There are two ways to write 12 as a product of two nontrivial divisors, i.e., 6*2 and 4*3. Since 8=6+2>4+3=7, we have a(12)=8.

Mathematica

Table[If[Length[Divisors[n]] > 2, Max[Table[Divisors[n][[j]] + n/Divisors[n][[j]], {j, 2, Length[Divisors[n]] - 1}]], n], {n, 1, 100}] (* Stefan Steinerberger, Feb 04 2008 *)

Crossrefs

Sequence in context: A337310 A001414 A134875 * A303702 A319057 A181894

Adjacent sequences: A134886 A134887 A134888 * A134890 A134891 A134892

Keyword

nonn,easy

Author

Joseph L. Pe, Feb 01 2008

Extensions

More terms from Stefan Steinerberger, Feb 04 2008

Status

approved